Qual è la derivata di # cosx ^ 3 #?
Risposta:
#-3x^2sinx^3#
Spiegazione:
Differentiate using the #color(blue)"chain rule"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x)).g'(x))color(white)(a/a)|))....(A)#
#f(g(x))=cos(x^3)rArrf'(g(x))=-sin(x^3)#
and #g(x)=x^3rArrg'(x)=3x^2#
#"----------------------------------------------------"#
Substitute these values in #color(red)"(A)"##rArrd/dx(cosx^3)=-sinx^3 .3x^2=-3x^2sinx^3#